I think mirod has the most efficient algorithm, trying successively longer substrings. Another implementation:

sub find_result {
   my $number = shift;
   my $prefix_length = length($number);
   my $result;

   1 until defined($result = $hash{substr($number, 0, $prefix_length--
+)})
      or $prefix_length <= 0;

   return $result;
}
[download]

This has the added benefit of allowing you to specify more specific mappings that take precedence over more generic. Another possibility might be constructing a tree of sorts, and walking the tree for each digit in your number:

%hash = (
  1 => {
     2 => {
        3 => 1,
        4 => 2,
     },
     3 => {
        2 => 3,
     }
   }
);

# Equivalent to ( 123 => 1, 124 => 2, 132 => 3 )

sub find_result {
   my $number = shift;
   my $position = 0;
   my $pointer = \%hash;

   while (defined(my $current = substr($number, $position++, 1))) {
      return $current unless ref($pointer->{$current});
      $pointer = $pointer->{$current};
   }

   return;
}
[download]

Creating this new tree-shaped %hash from a list of prefix => result pairs is an exercise for the reader.